Latest tweak to controversial bill requiring a higher pay floor on any city-subsidized projects would exempt businesses with less than $1 million in revenue and nonprofits of all sizes.

Proponents of a City Council bill that would require jobs resulting from city-subsidized projects to pay at least $10 an hour, plus benefits, are intensifying their campaign this week. They've crafted three amendments to make the measure more palatable to business and are staging a 1,000-person rally Thursday evening to draw on the symbolism of the upcoming holiday recognizing Dr. Martin Luther King Jr.

The amendments carve out three groups whose members have argued that the bill would have a harmful impact on their operations. Small businesses with less than $1 million a year in revenues, nonprofits of all sizes and certain employers on projects that are composed primarily of affordable housing will be exempted from the wage mandate, which was resubmitted to the Council this week.

The small business exemption was designed in part to appeal to City Council Speaker Christine Quinn, who will ultimately decide if the bill gets to a vote. Ms. Quinn has worked to burnish her small business credentials in advance of a potential run for City Hall in 2013. She nixed a labor-backed paid-sick-days bill last year, citing its potential to hurt small businesses. It wasn't immediately clear how many of the city's 200,000 small businesses would fall under the $1 million revenue threshold.

Supporters of the living wage measure have stepped up their efforts to sway the speaker— who has yet to take a public stance—to their side. A spokeswoman for Ms. Quinn declined to comment. Members of a clergy coalition backing the bill met with Ms. Quinn's staffers last week in an effort to make a religious case for the wage mandate.

“I've seen the impact these low-wage jobs have in a city where the cost of living is so high,” said Doug Cunningham, pastor at New Day United Methodist Church in the Bronx, who attended the meeting with the speaker's staff. “Sometimes top business leaders and officials don't understand what it's like to live in the city on these low-wage jobs. It affects every aspect of community and family life.”

The affordable housing amendment exempts some employers on projects where residential units comprise more than 75% of the project area and no less than 75% of the apartments are affordable to families earning less than 125% of the area's median income.

Also, Councilman Daniel Garodnick, D-Manhattan, signed on as the 29th sponsor of the bill, moving it closer to the 34-member supermajority needed to override a potential veto by Mayor Michael Bloomberg. Supporters said the imprimatur of Mr. Garodnick, known for an independent streak, showed that the campaign was gaining momentum among members outside the Council's progressive caucus.

Thursday's rally will be held at the Convent Avenue Baptist Church in Harlem and organizers say more than 1,000 supporters, including city Comptroller John Liu and Bronx Borough President Ruben Diaz Jr., are expected to attend. Religious leaders plan in their speeches to draw on the legacy of Dr. King, who was shot in Memphis while supporting low-wage sanitation workers.

Bloomberg administration officials have consistently argued that tying wage requirements to subsidies would squash development. The city's Economic Development Corp. retained a Boston-based consulting firm to conduct a $1 million study on the feasibility of mandates. That study is expected to be completed by March.

A spokesman for Mr. Bloomberg declined to comment on the revised bill, saying he had yet to see it. Deputy Mayor for Economic Development Robert Steel said in a speech last month that while the administration was “open-minded and looking forward to seeing the results of the study,” its philosophy remained clear: “When the city evaluates potential investments, the most important lens we will use is job creation. As the mayor has often said, ‘New York City has to be open for business.' ”